OUTLINE: This is a multicenter study. Regimen A: Patients receive gemcitabine IV over 30 minutes followed by cisplatin IV over 2 hours on day 1 and trastuzumab (Herceptin) IV over 90 minutes on day 2. Patients receive trastuzumab IV over 90 minutes followed by gemcitabine IV over 30 minutes on day 8 and trastuzumab IV over 90 minutes on day 15. Patients proceed to regimen B on day 22 of regimen A. Regimen B: Patients receive trastuzumab IV over 30-90 minutes, gemcitabine IV over 30 minutes, and cisplatin IV over 2 hours on day 1. Patients receive trastuzumab IV over 30-90 minutes followed by gemcitabine IV over 30 minutes on day 8 and trastuzumab IV over 30-90 minutes on day 15. Treatment repeats every 21 days for up to 5 courses in the absence of disease progression or unacceptable toxicity. Maintenance: After completion of 6 courses, patients with stable disease or partial response receive trastuzumab IV over 30-90 minutes weekly until tumor progression.